Finite Group Databasebeta

← Group #11922991

Character table — Group #11922991

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222333344444466666666668888888888881212121212121616161616161616161616161616161616161818181818181818363636363636363636363636
order12442346888812122244612242424242466888812123336661212121212126122424242466612121224242424242424242424242488888888224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-11-1111-1-1111111-1-111-1-1-1-11111-1-111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111-11-111-1-1-1-1-1-1
χ61111-11-1111-1-1111111-1-111-1-1-1-11111-1-111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111
χ71111-11-11-1-111111111-1-1-1-111-1-111-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-11-11-1-111-1-1-1-1
χ81111-11-11-1-111111111-1-1-1-111-1-111-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-111-1-11111
χ911-1-111-11i−ii−i-1-111-1-11-1i−ii−i1-111i−ii−i-1-1111111-1-1-1-1-1-11-1i−ii−i111-1-1-1iii−i−i−iiii−i−i−iii−i−iii−i−i1-1-111-11-1i−ii−i
χ1011-1-111-11i−ii−i-1-111-1-11-1i−ii−i1-111i−ii−i-1-1111111-1-1-1-1-1-11-1i−ii−i111-1-1-1iii−i−i−iiii−i−i−i−i−iii−i−iii-111-1-11-11−ii−ii
χ1111-1-111-11−ii−ii-1-111-1-11-1−ii−ii1-111−ii−ii-1-1111111-1-1-1-1-1-11-1−ii−ii111-1-1-1−i−i−iiii−i−i−iiiiii−i−iii−i−i-111-1-11-11i−ii−i
χ1211-1-111-11−ii−ii-1-111-1-11-1−ii−ii1-111−ii−ii-1-1111111-1-1-1-1-1-11-1−ii−ii111-1-1-1−i−i−iiii−i−i−iiii−i−iii−i−iii1-1-111-11-1−ii−ii
χ1311-1-1-1111i−i−ii-1-111-1-1-11i−i−ii-1111i−i−ii-1-1111111-1-1-1-1-1-1-11i−i−ii-1-1-1111iii−i−i−i−i−i−iiiiii−i−iii−i−i11-1-11-1-11−ii−ii
χ1411-1-1-1111i−i−ii-1-111-1-1-11i−i−ii-1111i−i−ii-1-1111111-1-1-1-1-1-1-11i−i−ii-1-1-1111iii−i−i−i−i−i−iiii−i−iii−i−iii-1-111-111-1i−ii−i
χ1511-1-1-1111−iii−i-1-111-1-1-11−iii−i-1111−iii−i-1-1111111-1-1-1-1-1-1-11−iii−i-1-1-1111−i−i−iiiiiii−i−i−iii−i−iii−i−i-1-111-111-1−ii−ii
χ1611-1-1-1111−iii−i-1-111-1-1-11−iii−i-1111−iii−i-1-1111111-1-1-1-1-1-1-11−iii−i-1-1-1111−i−i−iiiiiii−i−i−i−i−iii−i−iii11-1-11-1-11i−ii−i
χ172222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222-2-2-2-222222222-2-2-2-22222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-111111111111100000000000000000000
χ1922222-12-12222-1-12222-1-1-1-1-1-122-1-12222-1-12-1-12-1-122-1-1-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-12-1-12-1-100000000000000000000
χ2022222-12-12222-1-12222-1-1-1-1-1-122-1-12222-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-12-1-12-100000000000000000000
χ2122222-12-12222-1-12222-1-1-1-1-1-122-1-12222-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-12-1-1200000000000000000000
χ2222222-12-1-2-2-2-2-1-12222-1-1111122-1-1-2-2-2-2-1-12-1-12-1-122-1-1-1-1-1-111112-1-12-1-1-211-211-211-21100000000000000000000
χ2322222-12-1-2-2-2-2-1-12222-1-1111122-1-1-2-2-2-2-1-1-12-1-12-1-1-122-1-1-1-11111-12-1-12-11-211-211-211-2100000000000000000000
χ2422222-12-1-2-2-2-2-1-12222-1-1111122-1-1-2-2-2-2-1-1-1-12-1-12-1-1-1-122-1-11111-1-12-1-1211-211-211-211-200000000000000000000
χ252222-22-2222-2-2222222-2-222-2-2-2-22222-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2111111-1-1-1-1-1-111111100000000000000000000
χ262222-22-22-2-222222222-2-2-2-222-2-222-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222111111111111-1-1-1-1-1-100000000000000000000
χ272222-2-1-2-122-2-2-1-1222211-1-111-2-2-1-122-2-2-1-12-1-12-1-122-1-1-1-111-1-111-211-2112-1-12-1-1-211-21100000000000000000000
χ282222-2-1-2-122-2-2-1-1222211-1-111-2-2-1-122-2-2-1-1-12-1-12-1-1-122-1-111-1-1111-211-21-12-1-12-11-211-2100000000000000000000
χ292222-2-1-2-122-2-2-1-1222211-1-111-2-2-1-122-2-2-1-1-1-12-1-12-1-1-1-12211-1-11111-211-2-1-12-1-1211-211-200000000000000000000
χ302222-2-1-2-1-2-222-1-122221111-1-1-2-2-1-1-2-222-1-12-1-12-1-122-1-1-1-11111-1-1-211-211-211-2112-1-12-1-100000000000000000000
χ312222-2-1-2-1-2-222-1-122221111-1-1-2-2-1-1-2-222-1-1-12-1-12-1-1-122-1-11111-1-11-211-211-211-21-12-1-12-100000000000000000000
χ322222-2-1-2-1-2-222-1-122221111-1-1-2-2-1-1-2-222-1-1-1-12-1-12-1-1-1-1221111-1-111-211-211-211-2-1-12-1-1200000000000000000000
χ3322-2-222-222i−2i2i−2i-2-222-2-22-22i−2i2i−2i2-2222i−2i2i−2i-2-2-1-1-1-1-1-11111112-22i−2i2i−2i-1-1-1111−i−i−iiii−i−i−iiii00000000000000000000
χ3422-2-222-22−2i2i−2i2i-2-222-2-22-2−2i2i−2i2i2-222−2i2i−2i2i-2-2-1-1-1-1-1-11111112-2−2i2i−2i2i-1-1-1111iii−i−i−iiii−i−i−i00000000000000000000
χ3522-2-22-1-2-12i−2i2i−2i1122-2-2-11−ii−ii2-2-1-12i−2i2i−2i112-1-12-1-1-2-21111-11−ii−ii2-1-1-2112i−i−i−2iii2i−i−i−2iii00000000000000000000
χ3622-2-22-1-2-12i−2i2i−2i1122-2-2-11−ii−ii2-2-1-12i−2i2i−2i11-12-1-12-111-2-211-11−ii−ii-12-11-21−i2i−ii−2ii−i2i−ii−2ii00000000000000000000
χ3722-2-22-1-2-12i−2i2i−2i1122-2-2-11−ii−ii2-2-1-12i−2i2i−2i11-1-12-1-121111-2-2-11−ii−ii-1-1211-2−i−i2iii−2i−i−i2iii−2i00000000000000000000
χ3822-2-22-1-2-1−2i2i−2i2i1122-2-2-11i−ii−i2-2-1-1−2i2i−2i2i112-1-12-1-1-2-21111-11i−ii−i2-1-1-211−2iii2i−i−i−2iii2i−i−i00000000000000000000
χ3922-2-22-1-2-1−2i2i−2i2i1122-2-2-11i−ii−i2-2-1-1−2i2i−2i2i11-12-1-12-111-2-211-11i−ii−i-12-11-21i−2ii−i2i−ii−2ii−i2i−i00000000000000000000
χ4022-2-22-1-2-1−2i2i−2i2i1122-2-2-11i−ii−i2-2-1-1−2i2i−2i2i11-1-12-1-121111-2-2-11i−ii−i-1-1211-2ii−2i−i−i2iii−2i−i−i2i00000000000000000000
χ4122-2-2-22222i−2i−2i2i-2-222-2-2-222i−2i−2i2i-22222i−2i−2i2i-2-2-1-1-1-1-1-1111111-222i−2i−2i2i111-1-1-1−i−i−iiiiiii−i−i−i00000000000000000000
χ4222-2-2-2222−2i2i2i−2i-2-222-2-2-22−2i2i2i−2i-2222−2i2i2i−2i-2-2-1-1-1-1-1-1111111-22−2i2i2i−2i111-1-1-1iii−i−i−i−i−i−iiii00000000000000000000
χ4322-2-2-2-12-12i−2i−2i2i1122-2-21-1−iii−i-22-1-12i−2i−2i2i112-1-12-1-1-2-211111-1−iii−i-2112-1-12i−i−i−2iii−2iii2i−i−i00000000000000000000
χ4422-2-2-2-12-12i−2i−2i2i1122-2-21-1−iii−i-22-1-12i−2i−2i2i11-12-1-12-111-2-2111-1−iii−i1-21-12-1−i2i−ii−2iii−2ii−i2i−i00000000000000000000
χ4522-2-2-2-12-12i−2i−2i2i1122-2-21-1−iii−i-22-1-12i−2i−2i2i11-1-12-1-121111-2-21-1−iii−i11-2-1-12−i−i2iii−2iii−2i−i−i2i00000000000000000000
χ4622-2-2-2-12-1−2i2i2i−2i1122-2-21-1i−i−ii-22-1-1−2i2i2i−2i112-1-12-1-1-2-211111-1i−i−ii-2112-1-1−2iii2i−i−i2i−i−i−2iii00000000000000000000
χ4722-2-2-2-12-1−2i2i2i−2i1122-2-21-1i−i−ii-22-1-1−2i2i2i−2i11-12-1-12-111-2-2111-1i−i−ii1-21-12-1i−2ii−i2i−i−i2i−ii−2ii00000000000000000000
χ4822-2-2-2-12-1−2i2i2i−2i1122-2-21-1i−i−ii-22-1-1−2i2i2i−2i11-1-12-1-121111-2-21-1i−i−ii11-2-1-12ii−2i−i−i2i−i−i2iii−2i00000000000000000000
χ492-22i−2i020-200002i−2i2-22i−2i000000002-200002i−2i222-2-2-22i−2i2i−2i2i−2i0000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000
χ502-22i−2i020-200002i−2i2-22i−2i000000002-200002i−2i222-2-2-22i−2i2i−2i2i−2i000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ512-2−2i2i020-20000−2i2i2-2−2i2i000000002-20000−2i2i222-2-2-2−2i2i−2i2i−2i2i0000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000
χ522-2−2i2i020-20000−2i2i2-2−2i2i000000002-20000−2i2i222-2-2-2−2i2i−2i2i−2i2i000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000
χ5333333333333333-1-1-1-1333333-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-10000000000000000001111-1-1-1-11111-1-1-1-111-1-1
χ5433333333333333-1-1-1-1333333-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1000000000000000000-1-1-1-11111-1-1-1-11111-1-111
χ5533333333-3-3-3-333-1-1-1-133-3-3-3-3-1-1-1-11111-1-1000000000000-1-111110000000000000000001111-1-1-1-1-1-1-1-1111111-1-1
χ5633333333-3-3-3-333-1-1-1-133-3-3-3-3-1-1-1-11111-1-1000000000000-1-11111000000000000000000-1-1-1-111111111-1-1-1-1-1-111
χ573333-33-3333-3-333-1-1-1-1-3-333-3-311-1-1-1-111-1-100000000000011-1-1110000000000000000001111-1-1-1-11-11-1-1-111-1-111
χ583333-33-3333-3-333-1-1-1-1-3-333-3-311-1-1-1-111-1-100000000000011-1-111000000000000000000-1-1-1-11111-11-1111-1-111-1-1
χ593333-33-33-3-33333-1-1-1-1-3-3-3-33311-1-111-1-1-1-10000000000001111-1-10000000000000000001111-1-1-1-1-11-1111-1-1-1-111
χ603333-33-33-3-33333-1-1-1-1-3-3-3-33311-1-111-1-1-1-10000000000001111-1-1000000000000000000-1-1-1-111111-11-1-1-11111-1-1
χ6133-3-333-333i−3i3i−3i-3-3-1-1113-33i−3i3i−3i-11-1-1−ii−ii11000000000000-11−ii−ii000000000000000000ii−i−i−i−iii1-1-11-11-11i−i−ii
χ6233-3-333-333i−3i3i−3i-3-3-1-1113-33i−3i3i−3i-11-1-1−ii−ii11000000000000-11−ii−ii000000000000000000−i−iiiii−i−i-111-11-11-1−iii−i
χ6333-3-333-33−3i3i−3i3i-3-3-1-1113-3−3i3i−3i3i-11-1-1i−ii−i11000000000000-11i−ii−i000000000000000000ii−i−i−i−iii-111-11-11-1i−i−ii
χ6433-3-333-33−3i3i−3i3i-3-3-1-1113-3−3i3i−3i3i-11-1-1i−ii−i11000000000000-11i−ii−i000000000000000000−i−iiiii−i−i1-1-11-11-11−iii−i
χ6533-3-3-33333i−3i−3i3i-3-3-1-111-333i−3i−3i3i1-1-1-1−iii−i110000000000001-1−iii−i000000000000000000ii−i−i−i−iii11-1-1-111-1−iii−i
χ6633-3-3-33333i−3i−3i3i-3-3-1-111-333i−3i−3i3i1-1-1-1−iii−i110000000000001-1−iii−i000000000000000000−i−iiiii−i−i-1-1111-1-11i−i−ii
χ6733-3-3-3333−3i3i3i−3i-3-3-1-111-33−3i3i3i−3i1-1-1-1i−i−ii110000000000001-1i−i−ii000000000000000000ii−i−i−i−iii-1-1111-1-11−iii−i
χ6833-3-3-3333−3i3i3i−3i-3-3-1-111-33−3i3i3i−3i1-1-1-1i−i−ii110000000000001-1i−i−ii000000000000000000−i−iiiii−i−i11-1-1-111-1i−i−ii
χ694-44i−4i040-400004i−4i4-44i−4i000000004-400004i−4i-2-2-2222−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ704-44i−4i0-2020000−2i2i4-44i−4i00000000-220000−2i2i4-2-2-4224i−4i−2i2i−2i2i00000000000000000000000000000000000000000000
χ714-44i−4i0-2020000−2i2i4-44i−4i00000000-220000−2i2i-24-22-42−2i2i4i−4i−2i2i00000000000000000000000000000000000000000000
χ724-44i−4i0-2020000−2i2i4-44i−4i00000000-220000−2i2i-2-2422-4−2i2i−2i2i4i−4i00000000000000000000000000000000000000000000
χ734-4−4i4i040-40000−4i4i4-4−4i4i000000004-40000−4i4i-2-2-22222i−2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ744-4−4i4i0-20200002i−2i4-4−4i4i00000000-2200002i−2i4-2-2-422−4i4i2i−2i2i−2i00000000000000000000000000000000000000000000
χ754-4−4i4i0-20200002i−2i4-4−4i4i00000000-2200002i−2i-24-22-422i−2i−4i4i2i−2i00000000000000000000000000000000000000000000
χ764-4−4i4i0-20200002i−2i4-4−4i4i00000000-2200002i−2i-2-2422-42i−2i2i−2i−4i4i00000000000000000000000000000000000000000000
χ7766666-36-36666-3-3-2-2-2-2-3-3-3-3-3-3-2-211-2-2-2-21100000000000011111100000000000000000000000000000000000000
χ7866666-36-3-6-6-6-6-3-3-2-2-2-2-3-33333-2-21122221100000000000011-1-1-1-100000000000000000000000000000000000000
χ796666-6-3-6-366-6-6-3-3-2-2-2-233-3-3332211-2-22211000000000000-1-111-1-100000000000000000000000000000000000000
χ806666-6-3-6-3-6-666-3-3-2-2-2-23333-3-3221122-2-211000000000000-1-1-1-11100000000000000000000000000000000000000
χ8166-6-66-3-6-36i−6i6i−6i33-2-222-33−3i3i−3i3i-2211−2i2i−2i2i-1-10000000000001-1i−ii−i00000000000000000000000000000000000000
χ8266-6-66-3-6-3−6i6i−6i6i33-2-222-333i−3i3i−3i-22112i−2i2i−2i-1-10000000000001-1−ii−ii00000000000000000000000000000000000000
χ8366-6-6-6-36-36i−6i−6i6i33-2-2223-3−3i3i3i−3i2-211−2i2i2i−2i-1-1000000000000-11i−i−ii00000000000000000000000000000000000000
χ8466-6-6-6-36-3−6i6i6i−6i33-2-2223-33i−3i−3i3i2-2112i−2i−2i2i-1-1000000000000-11−iii−i00000000000000000000000000000000000000
χ856-66i−6i060-600006i−6i-22−2i2i00000000-220000−2i2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ866-66i−6i060-600006i−6i-22−2i2i00000000-220000−2i2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000
χ876-6−6i6i060-60000−6i6i-222i−2i00000000-2200002i−2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000
χ886-6−6i6i060-60000−6i6i-222i−2i00000000-2200002i−2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000
χ8912-1212i−12i0-6060000−6i6i-44−4i4i000000002-200002i−2i00000000000000000000000000000000000000000000000000000000
χ9012-12−12i12i0-60600006i−6i-444i−4i000000002-20000−2i2i00000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.